5.2.4.22 Various Problems on the Plane

A trapezoid with the sum of the lengths of the bases 18 and the sides equal to 3 and 5. The line \ (\ ell \) crosses the bases so that the trapezoid area is broken in half and the perimeters of two quadrangles, which are divided into trapezoid, apply as 8: 9. Find the length of the section of the straight \ (\ ell \), the ends of which lie on the basis of the trapezoid.